You are currently browsing the tag archive for the ‘Self belief’ tag.

“If I have seen a little further it is by standing on the shoulders of Giants”

Prior to Isaac Newton’s tribute (above) to Rene Descartes and Robert Hooke in a letter to the latter, it was reportedly the 12th century theologian and author John of Salisbury who was recorded as having used an even earlier version of this humbling admission—in a treatise on logic called Metalogicon, written in Latin in 1159, the gist of which is translatable as:

“Bernard of Chartres used to say that we are like dwarfs on the shoulders of giants, so that we can see more than they, and things at a greater distance, not by virtue of any sharpness of sight on our part, or any physical distinction, but because we are carried high and raised up by their giant size.

(Dicebat Bernardus Carnotensis nos esse quasi nanos, gigantium humeris insidentes, ut possimus plura eis et remotiora videre, non utique proprii visus acumine, aut eminentia corporis, sed quia in altum subvenimur et extollimur magnitudine gigantea.)”

Contrary to a contemporary interpretation of the remark:

$\bullet$ ‘standing on the shoulders of Giants’

as describing:

$\bullet$building on previous discoveries“,

it seems to me that what Bernard of Chartres apparently intended was to suggest that it doesn’t necessarily take a genius to see farther; only someone both humble and willing to:

$\bullet$ first, clamber onto the shoulders of a giant and have the self-belief to see things at first-hand as they appear from a higher perspective (achieved more by the nature of height—and the curvature of our immediate space as implicit in such an analogy—than by the nature of genius); and,

$\bullet$ second, avoid trying to see things first through the eyes of the giant upon whose shoulders one stands (for the giant might indeed be a vision-blinding genius)!

It was this latter lesson that I was incidentally taught by—and one of the few that I learnt (probably far too well for better or worse) from—one of my Giants, the late Professor Manohar S. Huzurbazaar, in my final year of graduation in 1964.

The occasion: I protested that the axiom of infinity (in the set theory course that he had just begun to teach us) was not self-evident to me, as (he had explained in his introductory lecture) an axiom should seem if a formal theory were to make any kind of coherent sense under interpretation.

Whilst clarifying that his actual instruction to us had not been that an axiom should necessarily ‘seem’ self-evident, but only that it should ‘be treated’ as self-evident, Professor Huzurbazar further agreed that the set-theoretical axiom of infinity was not really as self-evident as an axiom ideally ought to seem in order to be treated as self-evident.

To my natural response asking him if it seemed at all self-evident to him, he replied in the negative; adding, however, that he believed it to be ‘true’ despite its lack of an unarguable element of ‘self-evidence’.

It was his remarkably candid response to my incredulous—and youthfully indiscreet—query as to how an unimpeachably objective person such as he (which was his defining characteristic) could hold such a subjective belief that has shaped my thinking ever since.

He said that he had ‘had’ to believe the axiom to be ‘true’, since he could not teach us what he did with ‘conviction’ if he did not have such faith!

Although I did not grasp it then, over the years I came to the realisation that committing to such a belief was the price he had willingly paid for a responsibility that he had recognised—and accepted—consciously at a very early age in his life (when he was tutoring his school going nephew, the renowned physicist Jayant V. Narlikar):

Nature had endowed him with the rare gift shared by great teachers—the capacity to reach out to, and inspire, students to learn beyond their instruction!

It was a responsibility that he bore unflinchingly and uncompromisingly, eventually becoming one of the most respected and sought after teachers (of his times in India) of Modern Algebra (now Category Theory), Set Theory and Analysis at both the graduate and post-graduate levels.

At the time, however, Professor Huzurbazar pointedly stressed that his belief should not influence me into believing the axiom to be true, nor into holding it as self-evident.

His words—spoken softly as was his wont—were:

“Challenge it”.

Although I chose not to follow an academic career, he never faltered in encouraging me to question the accepted paradigms of the day when I shared the direction of my reading and thinking (particularly on Logic and the Foundations of Mathematics) with him on the few occasions that I met him over the next twenty years.

Moreover, even if the desired self-evident nature of the most fundamental axioms of mathematics (those of first-order Peano Arithmetic and Computability Theory) were to be shown as formally inconsistent with a belief in the ‘self-evident’ truth of the axiom of infinity (a goal that continues to motivate me), I believe that the shades of Professor Huzurbazaar would feel more liberated than bruised by the ‘fall’.

What you believe can make a difference only if you believe that it will

I received a somewhat disturbing email today, forwarded without any (but presumably would be favourable) comments, and purportedly quoting political content that I perceived as slanted even if not wholly inaccurate.

My instinctive reaction for years has been to immediately delete such mails, consigning most senders to a junk labelled category, and sparing a few out of deference to an existing relationship.

It was only after deleting todays mail that I fleetingly felt my instinctive response did justice neither to my relationship with, nor to my regard for, the sender.

I immediately recovered the mail and started reflecting on what had given me pause.

I certainly owed the sender (indisputably a well-wisher) a more appropriate response; so why was the response not obvious?

Was it that with each passing year we find it increasingly difficult to believe that our beliefs can make a difference to even those whom we know we influence?

That’s surely not a trap that I would like to fall into without protest; so here was my laboured—and deliberately excessively detailed—protest to the sender!

1. The substance of the mail you forwarded was published on an internet discussion group forum titled ‘FunOnTheNetCommunity’.

2. The source of the particular commentary in “This is such a sad commentary on Congress misrule” email, seemingly attributable to ‘Mark Tully’, is actually this post titled “Mark Tully British turned Indian intent on agitating?”, contributed on June 14, 2012, 02:55:49 PM by ‘Seshamurthy’.

3. Seshamurthy has given his own bio-data as:

Name: Seshamurthy
Posts: 25351 (12.342 per day)
Topics started: 5085
Position: FOTN Junky
Stars
Karma: 4514
Date Registered: December 24, 2007, 11:18:43 PM
Last Active: Today at 04:48:07 PM
________________________________________
Gender: Male
Age: N/A
Location: India
Local Time: August 09, 2013, 05:12:08 PM
________________________________________
ICQ:
AIM:
MSN:
YIM:
Email: hidden
User Images: View Gallery
Website:
Mood: none
Current Status: Offline
________________________________________
Signature:

4. Seshamurthy’s post was moderated on behalf of the blog (i.e. cleared for posting as not obviously offensive legally to readers of the blog) by the following three persons:

(i) Name: Cynthia
Posts: 14662 (5.222 per day)
Topics started: 1981
Position: FOTN Hero
Stars
Karma: 1865
Date Registered: December 01, 2005, 05:37:59 AM
Last Active: August 29, 2011, 05:17:30 PM
________________________________________
Gender: Female
Age: N/A
Location: Jakarta,Indonesia
Local Time: August 09, 2013, 05:18:55 PM
________________________________________
ICQ:
AIM:
MSN:
YIM:
Email: hidden
User Images: View Gallery
Website:
Mood: atpeace
Current Status: Offline
________________________________________
Signature:

(ii) Name: *Chinny*
Custom Title: The Woman behind those Beautiful Words…
Posts: 9042 (3.849 per day)
Topics started: 788
Position: FOTN Hero
Stars
Karma: 1634
Date Registered: March 04, 2007, 06:39:27 PM
Last Active: May 30, 2013, 07:35:13 AM
________________________________________
Real name: Ashtoreth Eros Chinea Yu Rosales Chui
Gender: Female
Age: 28
Location: ShaTin HongKong
Sports/Games: Pool (Billiards)
Local Time: August 09, 2013, 05:20:48 PM
________________________________________
ICQ:
AIM:
MSN:
YIM:
Email: hidden
User Images: View Gallery
Website: http://chinchinchinny.multiply.com/
Mood: blue
Current Status: Offline
________________________________________
Signature: I Wonder WHY?…

(iii)
Name: Anand VP
Posts: 19648 (8.379 per day)
Topics started: 1741
Position: FOTN Junky
Stars
Karma: 7047
Date Registered: March 09, 2007, 12:32:17 AM
Last Active: Today at 01:54:47 AM
________________________________________
Gender: Male
Age: N/A
Location: Gorakhpur
Local Time: August 09, 2013, 05:24:27 PM
________________________________________
ICQ:
AIM:
MSN:
YIM:
Email: hidden
User Images: View Gallery
Website:
Mood: contemplative
Current Status: Offline
________________________________________
Signature: *”Rising to eminence by merit, you will live respected & die, regretted!”

5. There are 5 comments to this post (not necessarily by regular readers of the blog):

(i) (Two very approving emoticons)

Full of facts! Pseudo-secularism and dynasty politics are bane of India; Mark Tully is largely correct that appeasement of minorities and vote bank politics continue to harm the nation socially and economically.

Re-establishment of Chhatrapati Sivaji’s Hindu Rashtra is the only way out, where all religions will be respected, no appeasement policies or pseudo-secularism will be practised, religious extremism and all kinds of terrorism will be mercilessly wiped out, minorities will have dignified co-existence with the majority Hindus with a sense of pride and spirit of harmony, conversion attempts by dubious means are banned, National security is assured and above all the benefits of ancient Hindu wisdom will be put to use for the benefit of not just India, but the entire world. May the day come soon! May India become once again the beacon of hope for the entire mankind!

+K, Sir!

(ii) (No emoticon)

Thanks Rajasekhar Iyer fr the visit and the add

(iii) (Indulgent emoticon only)

(iv) (Indulgent emoticon only)

(v) (Quizzical emoticon)

shesha u didnt put the source page link?

Rather than simply forwarding such mail, you should seriously consider directly commenting on the post in the web-page itself (as the above 5 have done), and/or forwarding only the link to the web –page source from where it originates, so that the persons receiving your mail can determine the veracity and authority of the source and its contents for themselves.

7. Why?

That way you will have a chance to strengthen the views of the author if you approve, moderate them if you do not (and, incidentally, avoid antagonising those who hold views that conflict with yours).

8. Cumulatively, such actions impact positively on society as a whole.

Reason: The more approvals on a post, the more likely it is to influence society since the post will be more likely to be given a higher priority (i.e. appear near the top of a search) in search engines such as Google whenever someone searches for a key word that occurs significantly in the post.

9. For instance, this link to a more reliable source for details of Mark Tully and his articles etc. is near the top of any search containing the words `Mark Tully’.

10. Click this link to see the sources for the information on the Wikipedia ‘Mark Tully’ page.

11. Click this link to see the credentials of the persons who have so far compiled and/or edited the data on this page (their bio-data is generally obtainable by clicking on their user names given in each entry).

I conclude that the message John Donne intended to convey by his powerful imagery in `No man is an island’ was perhaps also that:

My life does make a difference to the universe, even if I choose to believe that it doesn’t!

There is even a scientific perspective on this—it’s known as the Butterfly Effect!

### Start here

Join 85 other followers

Diagonal Argument

Math, science, their history, and assorted trivia and quadrivia.

math - update

blogging & searching for true math ...

George Lakoff

George Lakoff has retired as Distinguished Professor of Cognitive Science and Linguistics at the University of California at Berkeley. He is now Director of the Center for the Neural Mind & Society (cnms.berkeley.edu).

LobeLog

Critical Perspectives on U.S. Foreign Policy

What's new

Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao

Quanta Magazine

Reviewing classical interpretations of Cantor's, Gödel's, Tarski's, and Turing's reasoning and addressing some grey areas in the foundations of mathematics, logic and computability

The Brains Blog

Since 2005, a leading forum for work in the philosophy and science of mind

Logic Matters

Reviewing classical interpretations of Cantor's, Gödel's, Tarski's, and Turing's reasoning and addressing some grey areas in the foundations of mathematics, logic and computability

A Neighborhood of Infinity

Reviewing classical interpretations of Cantor's, Gödel's, Tarski's, and Turing's reasoning and addressing some grey areas in the foundations of mathematics, logic and computability

Combinatorics and more

Gil Kalai's blog

Mathematics and Computation

Reviewing classical interpretations of Cantor's, Gödel's, Tarski's, and Turing's reasoning and addressing some grey areas in the foundations of mathematics, logic and computability

Foundations of Mathematics, Logic & Computability

Reviewing classical interpretations of Cantor's, Gödel's, Tarski's, and Turing's reasoning and addressing some grey areas in the foundations of mathematics, logic and computability

John D. Cook

Reviewing classical interpretations of Cantor's, Gödel's, Tarski's, and Turing's reasoning and addressing some grey areas in the foundations of mathematics, logic and computability

Shtetl-Optimized

Reviewing classical interpretations of Cantor's, Gödel's, Tarski's, and Turing's reasoning and addressing some grey areas in the foundations of mathematics, logic and computability

Nanoexplanations

the blog of Aaron Sterling

Eric Cavalcanti

Quantum physicist

East Asia Forum

Reviewing classical interpretations of Cantor's, Gödel's, Tarski's, and Turing's reasoning and addressing some grey areas in the foundations of mathematics, logic and computability